Why can I not achieve a smooth surface when subdividing?
I took a default sphere with 32 segments



Into edit mode and select a single vertex. When selected then bevel it ctrlshiftb



with the faces still selected right click and select loop tools. If you do not have them then they are in the add ons (google how to use add ons from preferences). Select circle



this will give you a nice circle shape to work from.



Add knife cuts as shown or alternatively select the two verticies you want to join and press j



Select the circle edges and ctrlshiftr to offset the edge loop you have selected. This will give you 2 new edge loops.



Select the inner faces and extrude inwards three times using the normal orientation 



You will end up with this topology



Add a subdivision surface modifier x 2 and set the auto smooth to 60



You can put it into a circular array and tweak the depth/scale of the hole